Mathematics & Computer Science
Angelo Rizzieri
I am a math and computer science student at the University of Chicago, a software engineer at Armatus Capital, and a mathematics researcher.
Chicago, Illinois
A rational turn closes the orbit after 5 reflections. The same path repeats.
Any expression: 1/3, 0.25, sqrt2, pi/4. Whole turns wrap around.
01 Research
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Billiards, Dynamics, and Geometry
Work in progressAn expository paper on how the geometry of a table shapes a billiard's trajectory, from circular and polygonal tables to translation surfaces and the illumination problem.
A closer look at the mathematics
For a circular table, the orbit is periodic when the angle between successive impact points is a rational multiple of 2π; otherwise, those impact points are dense on the boundary. On the torus we use Weyl equidistribution to prove a trajectory of irrational slope meets a region in proportion to its area. We then code trajectories as infinite words, prove the Morse-Hedlund classification, and show an irrational slope gives complexity k+1, so the coding is Sturmian. The last sections construct translation surfaces from polygons glued in parallel pairs, define the SL(2,R) action and the Veech group, and take up the illumination problem following Hubert, Schmoll, and Troubetzkoy.
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Feasibility Bound for the Invariant-Based Rank-1 OCRS in the Adversarial Order Model
α ≤ ½The bound is tight, and a
known construction reaches it.An online contention resolution scheme decides item by item, and permanently, whether to accept what arrives. I proved that in the rank 1 matroid setting with adversarial ordering, feasibility forces the selection guarantee to α ≤ ½. Combined with the known construction that achieves ½, this pins the scheme at exactly ½ selectable. Every active item gets a 50% chance of acceptance, and no scheme of this form does better.
02 Selected projects
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TRACE
January 2026Explains why a stock moved
A scoring model with eight factors, built on data from six financial APIs. It constructs and ranks causal graphs that explain a stock's price movement on a given day. FastAPI backend, React frontend, with results streamed to the browser as they are computed.
Each candidate cause is scored on eight factors. The graphs are then ranked by how much of the day's move they account for. -
Site Memory
2026Chrome extension, published on the Chrome Web Store
Saves your text highlights and notes on any web page or PDF, then restores them automatically the next time you visit. Highlights re-anchor themselves, so they survive changes to the page. Everything is stored on your own device. No accounts, no syncing, no tracking.
The highlight is written to local storage, then re-anchored to the same text when you come back. -
Google Drive Search Agent
February 2026Answers questions about your documents
An agent that searches Google Drive and answers questions about what it finds, across more than 10 file types. It runs a tool loop: search, open a file, read it, then repeat until it can answer. Caching the prompt and the tool results cut inference cost by about 90%, measured with an eval harness that scores each system prompt on token count and answer correctness.
The model picks a tool, reads the result, and repeats until it can answer. Not hosted online. Reading a visitor's Drive needs Google's restricted scope verification, so the agent runs locally with your own credentials. Setup steps are in the README.
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Do LLMs Sample Randomly?
December 2025An experiment on how models pick numbers
1,000 API calls testing whether a model gives a less biased number when asked to hide one inside a story, compared to asking for a number directly. Both methods fail a chi square test against a uniform distribution (p < 0.001), but the gap is large. Direct requests return 7 in 94.6% of samples, compared to 31.2% when the number is embedded in a story.
How often the model chose 7 Asked directly94.6%Inside a story31.2%Both prompts still favor 7.
03 Experience
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July 2026 to Present
Armatus Capital
Software Engineering Intern, LLM Infrastructure and Data Platform
- Built and deployed a financial analytics platform with over 3,400 automated tests. It turns daily market data for over 3,200 equities into six visualization tools used daily by a portfolio manager.
- Mined 3,152 SEC filings into a knowledge graph of 2,390 supply-chain relationships.
- Cut LLM pipeline latency from 14 minutes to under 5 without increasing the request rate, using a shared pacer and concurrent processing.
- Modeled inference costs across 21 production runs and uncovered a cache-key issue that had prevented reuse of a 170,000-token prompt prefix.
- Cut false positives in a market-signal detector from 3.8 per day to 0.03 per day, and built a 30-rule gate that checks every model-generated claim against its source.
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June to September 2026
University of Chicago
Researcher (REU), Topological Dynamical Systems
- Studying illumination problems in mathematical billiards and Veech surfaces under Dr. Tina Torkaman.
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June to September 2025
University of Chicago
Researcher, Algorithmic Game Theory
- Proved a tight optimality bound for online contention resolution schemes on rank 1 matroids, a framework used in auction design and online pricing under uncertainty.
- Constructed a matching algorithm that achieves the bound, confirming that 50% acceptance probability is exactly optimal under adversarial ordering.
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October 2025 to Present
Maroon Capital
Analyst, UChicago quantitative finance and trading club
- Developed a systematic trading strategy that placed 1st out of 13 teams in the club competition.
- Built a stock screener that uses regression on company fundamentals to flag potentially mispriced stocks.
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September 2025 to Present
University of Chicago
Course Assistant, Calculus I to III
- Grade weekly problem sets for over 60 students per quarter.
04 Background
Education
University of Chicago
B.S. Mathematics and Computer Science, 2028
Honors Combinatorics, Real Analysis I to III, Probability, Abstract Linear Algebra, Systems Programming
Honors
- Harvard Trading Competition
3rd place, Jump Trading Challenge 2026 - UChicago Hackathon
Finalist 2026 - PicoCTF
135th out of 10,460 teams 2023 to 2025
Skills
- Languages
- Python, JavaScript, TypeScript, SQL, R, Java, C
- Data and ML
- NumPy, pandas, statsmodels, SciPy, PyTorch, HuggingFace Transformers
- Tools
- React, FastAPI, Flask, Node.js, REST APIs, LLM APIs, Vercel, Git, Linux, LaTeX